Math 4606, Summer '04

Last changed: Aug 8, 2004.

This course is a proof-oriented version of one- and several-variable Calculus.

The course meets 7 hours a week:
11:15-12:05 MWF, and
11:15-1:05 TuTh (break: 12:05-12:20), always in AmundH 116.

Our TEXT is Basic Elements of Real Analysis, by Murray H. Protter.
ISBN 0-387-98479-8
DON'T buy Buck's Advanced Calculus!

The text may be late arriving, but that doesn't matter much; we will start wih some material on Logic and Sets that is not in the text anyway.

Office Hours: 12:20 - 1:05 MWF and "on demand": just after class TuTh. Otherwise, by appointment -- or call 5-3855 to see if I'm in and available, especially before class.

You can ask questions by email too: jodeit@math.umn.edu
Please, send me messages in TEXT mode only! Also, here is a Web link to a list of special codes for math symbols (most of them start with the \ character).


Announcements, hints, "news" will be here.

News August 8: I'll be in my office, VinH 258, Monday from about 11:15
to about 12:30. Call if you plan to come late!

News August 6: Grades were sent to the Registrar
at about 6pm today. If you can't get your grade online that way
after 6pm tomorrow, let me know!

Good luck to you all! I'll miss you; I'll be in my office Monday
for a while, and I'll post when Sunday night, probably.


News August 5: Here is the list of Final A GPAs
2D -*- 2.69 -*- 2.8064
2S -*- 4.59 -*- 4.2416
3D -*- 2.41 -*- 2.7232
3H -*- 3.37 -*- 3.0121
3S -*- 3.18 -*- 3.8357
4S -*- 2.31 -*- 2.6919
5C -*- 3.01 -*- 2.9033
5D -*- 2.34 -*- 2.0016
6D -*- 0.56 -*- 1.6529
7H -*- 4.12 -*- 3.4027
8C -*- 2.80 -*- 2.8391
8S -*- 3.08 -*- 2.9238
9C -*- 2.23 -*- 2.6681
9H -*- 3.73 -*- 2.9819
AC -*- 0.78 -*- 2.1832
AS -*- 2.09 -*- 2.6754
JC -*- 1.78 -*- 3.1438
JH -*- 1.33 -*- 2.5546
JS -*- 0.66 -*- 2.4580
KD -*- 2.05 -*- 2.6522
KH -*- 3.55 -*- 3.5192
TC -*- 2.45 -*- 2.9106
TS -*- 2.45 -*- 2.9416

NOTES: The first number is the Final A GPA. The second one is the
(unfinished) Course GPA so far -- I'll update it later tonight -- by about
9pm maybe -- it will not be lower than the one you see...

10:15pm Aug 5: I did not change any gradelines, so the Grade-so-far number
has not changed.


News August 4: (Each part of) the Final will have 10 problems, but only 8
will be scored. MOREOVER, the first 8 solutions will be scored!
Thus if you want an answer ignored, you must write the word OMIT on it in a
prominent place!!! Otherwise, if it's already scored and OMIT is on the back of
the page, it will still count!!! This is because I have to use time wisely to
get the scores on the Web in a timely manner.

Some questions asked (answered here, not when asked): Is the Final going to be harder that the Quizzes?
Yes and No: Some questions will essentially be
Quiz questions; others will not be, but may be easier or harder, depending on
what you have absorbed. Thus, read all the questions, making priority marks as you go,
writing out Definitions and Theorem statements as you go.

Can we be asked to prove Theorems from the book?
Yes, especially when the proof given in class was short.

Note: Treat your self well, be rested! The next News won't be until late tonight.
in the second column is unchanged.

News August 2: Quiz 7 Solutions: posted.
The Final will have 2 parts, one on Thursday after the
break, which will be earlier than usual, the other on
Friday at 11:15. Challenge problems must be turned in
Thursday by 11:15 sharp!

News July 28a: Assignments have been updated!!
Two handouts are posted. They were written
hastily so they offer good typo hunting!
Special Problems 8 and 9 are posted.

News July 26: Quiz 6 Solutions: posted.

News July 23: See information on Challenge Problems below.
Assignments have been updated. The last papergrader assignment is due
July 29. More Special Problems will be assigned - 2, maybe 3.

News July 20: A solution for Special problem 6 has been posted.

News July 19: Solutions for Quiz 5 have been posted.
Some News items have been moved to Old News (link below).
Here are Quiz gradelines:
p-top 50 50
A     40 39
B     30 28
C     20 17
D     15 14
The first list is for Quiz 1. The other one is for
all the others, except that Quiz 3 has a p-top of 60.
News July 14: Assignments have been updated.
A solution for Special Problem 4 has been posted.


News July 12: Solutions for Quiz 4 have been posted.
Because of approved late papers the solution of SP #4 will be posted
Wednesday after class.


News July 9: Some remarks/hints on the redo of SP #4
that is due Monday:
The sequence {r_n} is given; you need to choose a strictly increasing
sequence {n_j} of natural numbers such that {r_{n_j}} converges to x-bar.
One way to do this is to make your chosen rationals also increase.
But your choices must be    s p e c i f i c!   It not enough
to simply say this "can be done;" you have to say exactly how to do it!
It   i s   OK to say you can pick, as one subsequence, all of the
r_n's   that lie between two numbers. But then in that one, you have to give
exact directions as to how to proceed! Thus the hints given in class:   n/(n+1)
increases strictly to one (this hint does not make sense until you get to the right
place to use it!)   and   Every non-empty subset of the natural numbers
has a least element (this hint is to assist you in choosing the next   n_j).


Challenge Problems are intended to be a vehicle for those who wish
to improve a Quiz GPA. If you are not confident that you have begun to master
understanding how to make proofs, you should not attempt one.

You must not work on a Challenge Problem with anone else. I will only answer
"clarification" questions. You must include a signed statement that you did not
work with, or consult with,   a n y o n e.   However, you   m a y
consult books. If you do, you must correctly cite what you use from the book.
You may not copy any proofs -- you must express what you use from the literature
in your own words.

You may only turn in one Challenge Problem, by Thursday August 5 at 11:15 in class.
All the standards for Special Problems apply, amplified(!), to Challenge Problems.
In particular, I will look for correct handling of definitions.
Proofs must be complete, without prolixity.

Two Challenge Problems are offered:

(1) Prove the "infinity-over-infinity, at infinity" case of l'Hospital's Rule.
A careful, FORMAL statement of the Theorem is required.


(2) Prove that every Darboux integrable function is Riemann integrable.
A careful, FORMAL statement of the Theorem is required.



Old News.  7/19



Links, if any, to other Web pages pages related to this course will go here. They are PDF files (you need Adobe Acrobat Reader to view them). Follow this link to download the latest Acrobat Reader from Adobe at no charge.
"Express" URL


   Math 4606 SS '04: Syllabus.

   Math 4606 SS '04: Assignments. 7/28


    A closed bounded set that's not compact. (because it's infinite-dimensional). 7/28

    On differentiation in the vector context. Examples. 7/28

    Quiz 7 solutions. 8/2

    Quiz 6 solutions. 7/26

    A solution for Special Problem 6. 7/20

    Quiz 5 solutions. 7/19

    A solution for Special Problem 4. 7/14

    Quiz 4 solutions. 7/12

    Quiz 3 solutions. 7/6

    Quiz 2 solutions. 6/28

    The Intermediate Value Theorem.

    The nth-root Theorem.

    Inductive Sets and Recursion.

    Axioms for the Real Numbers.

Below: background material from a much earlier version of this course

  Introduction

  Mathematical Logic

  Sets, variables and quantifiers

  Logic and sets



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